2068 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 33, NO. 10, …€¦ · available polymer and switchable materials that achieve ex-cellent optical properties both for narrowband and broadband

2068 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 33, NO. 10, MAY 15, 2015

Nonmechanical Laser Beam Steering Based onPolymer Polarization Gratings: Design Optimization

and DemonstrationJihwan Kim, Member, IEEE, Matthew N. Miskiewicz, Member, IEEE, Steve Serati,

and Michael J. Escuti, Member, IEEE

Abstract—We present a wide-angle, nonmechanical laser beamsteerer based on polymer polarization gratings with an optimaldesign approach for maximizing field-of-regard (FOR). The steer-ing design offers exponential scaling of the number of steeringangles, called suprabinary steering. The design approach can beeasily adapted for any 1-D or 2-D (e.g., symmetric or asymmetricFOR) beam steering. We simulate a system using a finite differenceand ray tracing tools and fabricate coarse beam steerer with 65◦

FOR with ∼8◦ resolution at 1550 nm. We demonstrate high opti-cal throughput (84%–87%) that can be substantially improved byoptimizing substrates and electrode materials. This beam steerercan achieve very low sidelobes and supports comparatively largebeam diameters paired with a very thin assembly and low beamwalk-off. We also demonstrate using a certain type of LC variableretarder that the total switching time from any steering angle toanother can be 1.7 ms or better.

Index Terms—Beam steering, diffractive optics, holography, li-dar, liquid crystals, optical communications, polarization grating,radar.

I. INTRODUCTION

THE fields of laser communications, directed energy, laserdetection and ranging (i.e., LADAR), and laser defensivecountermeasures are in various stages of development. A greatchallenge for these advanced laser systems is the ability to ac-curately and efficiently steer optical beams over a large fieldof regard (FOR) without interfering with other platform func-tions. Conventionally, a mechanical gimbal (e.g., optical turretor pod) is used to steer optical beams to cover large FOR, butthe use of the gimbal is limiting due to its mechanical instabilityand space requirements, especially for smaller platforms suchas unmanned airborne vehicles.

Nonmechanical steering of electromagnetic radiationpromises significant benefits to many applications, especially

Manuscript received August 18, 2014; revised December 12, 2014; acceptedJanuary 1, 2015. Date of publication January 13, 2015; date of current versionMarch 16, 2015. This work was supported by the National Science Foundationunder (NSF Grant ECCS-0955127) and also supported by the National ScienceFoundation (CAREER award ECCS-0955127), by Merck Chemicals Ltd. foraccess to the RMS materials, by Bennett Aerospace for the SLCVR, and byLambda Research Corp. for TracePro education discount and support.

J. Kim, M. N. Miskiewicz, and M. J. Escuti are with the Department of Electri-cal and Computer Engineering, North Carolina State University, Raleigh, NorthCarolina, CA 27695 USA (e-mail: [email protected]; [email protected];[email protected]).

S. Serati is with the Boulder Nonlinear Systems Inc., Lafayette, CO 80026USA (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JLT.2015.2392694

those where precise beam pointing and tracking are requiredwithin a compact unit in systems [1], [2]. Many nonmechanicalsteering techniques [3]–[11] have been studied, but all of theseapproaches are limited by one or more of the following reasons:low throughput, scattering, small steering angle/aperture, andlarge physical size/weight. Shi and coworkers have shown highefficiency nonmechanical steering utilizing a liquid crystal (LC)phase grating [12], but the technique was limited to small anglesand slow speeds.

In order to realize a fast and low loss nonmechanical beamsteering, we introduced a technique based on switchable polar-ization gratings (PGs) [13], [14]. This technique utilizes a stackof switchable PGs and waveplates (WPs). Later, we introduced aclosely related system for wide angle steering based on polymerPGs, called Supra-Binary (SB) steering [15].

Here, we introduce an optimal design approach of the SBsteering for 1D/2D. This optimization can be easily adapted forany 2D beam steering (e.g., symmetric or asymmetric FOR).Using finite-difference (Wolfsim-3D [16]) and ray-tracing (Tra-cePro) tools, we simulate the non-ideal behavior of PGs and anoptimized SB steering configuration. Lastly, we experimentallyfabricate and evaluate a 1D SB beam steerer at 1550 nm forwide FOR (e.g., 65◦) with fairly high throughput (e.g., > 85%).

II. BACKGROUND

A. Polarization Gratings

The key element of our approach is a PG, which is composedof a continuous, in-plane, bend-splay profile of spatially vary-ing optical axis formed with birefringent materials [17], [18].These PGs manifest unique behaviors, including 100% theoret-ical efficiency into a single diffraction order and a wide angularacceptance angle. The first order diffraction efficiency can beexpressed as [19]

η±1 = (1/2)(1 ∓ S ′3) sin2(Γ/2), (1)

where ηm is the diffraction efficiency of the order m, Γ =2πΔnd/λ is the retardation of the LC layer, λ is the wave-length of the incident light, and S ′3 = S3/S0 is the normalizedStokes parameter describing the ellipticity of the incident light.Note that an incident beam is diffracted into only one of thefirst orders when input is circularly polarized (i.e., S ′3 = ±1)and the retardation of the LC layer is halfwave (Δnd = λ/2).For incident light that is coplanar with the grating vector, thefirst order diffraction angle is governed by the classic grating

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KIM et al.: NONMECHANICAL LASER BEAM STEERING BASED ON POLYMER POLARIZATION GRATINGS 2069

Fig. 1. Conical diffraction of the PG: (a) Non-coplanar incidence on the PG.Output diffraction (m = 0,±1) of the PG presented in (b) real space and (c)direction cosine space.

equation,

θm = sin−1(mλ/Λ + sin θin ), (2)

where θin is the incident angle, θm is the first order diffrac-tion angle, the order m = {+1,−1} depends on the incidentpolarization, and Λ is the grating period.

High quality PGs have been demonstrated in commerciallyavailable polymer and switchable materials that achieve ex-cellent optical properties both for narrowband and broadbandwavelength operation [20].

B. Conical Diffraction of PGs

Whenever incident light is not coplanar with the grating vec-tor, the result is the so called conical diffraction behavior asshown in Fig. 1(a). Since the angle relationship between theinput and output is nonlinear, it is convenient to introduce adirection cosine space where diffraction at an arbitrary incidentangle can be described by simple, linear vector representations[21]. The direction cosines of the steered beam are given by

αm = (mλ/Λ) cos Ψ + sin θin cos φin (3a)

βm = (mλ/Λ) sin Ψ + sin θin sin φin (3b)

γm =√

1 − α2m − β2m , (3c)

Fig. 2. Total number of steering angle comparison: binary [13] (dotted),ternary [14] (dashed), and SB [15] (solid). The binary and ternary requiretwo LC elements in a single steering stage, which can steer 2N +1 − 1 and 3Nangles respectively with N stages, while the SB can steer 4N angles with thesame number of LC elements.

where Ψ is the azimuth angle of the PG’s grating vector, θinis the polar angle of the incident beam, and φin is the azimuthangle of the incident beam. By definition, α2m + β

2m ≤ 1. The

net azimuth and polar angles of the transmitted beam can bedetermined from Eq. (3) as

φm = tan−1 (βm /αm ) (4a)

θm = cos−1 (γm ) . (4b)

Examples of conical diffraction are shown in real space (seeFig. 1(b)) and direction cosine space (see Fig. 1(c)) for obliqueincidence (e.g., {θin , φin}= {−45◦ − 45◦, 0}) on the PG whenΨ = 90◦ and λ/Λ = 0.5 (i.e., 30◦ diffraction angle). Since theoutput beam direction can be described as a simple vector sumof the incident and the PG diffraction components, the directioncosine space representation makes it easy to determine designparameters relevant to beam steering systems.

C. Steering Design Comparison

It is possible to configure PG steering designs that are basedon either switchable [13], [14] or polymer [15] PGs. These de-signs all utilize at least one switchable LC variable retarder asthe polarization selector/controller before each PG, which isneeded to access the full FOR. But the LC elements, includ-ing the switchable PG are the main cause of loss of the steeringsystems, due to the absorption and reflection of transparent elec-trode (e.g., indium tin oxide) and the typically smaller scatteringcaused by LC itself. Therefore, when optimizing transmittanceand efficiency, fewer LC elements is preferred. With this inmind, the number of LC elements in a design can be used as abenchmark of the system’s performance.

Fig. 2 shows total number of steering angles of the threedifferent steering designs. For every given number of desiredsteering angles, SB designs based on polymer PGs are likelyto perform the best, having the highest number per LC ele-ment ratio. Another important benefit of polymer PGs is theirexpected lifetime and stability at high temperatures. Moreover,since polymer PGs typically have lower scattering and higherefficiency than switchable PGs, the SB design has an additionaladvantage over the switchable-PG based designs. In sum, we


Fig. 3. A concept of wide-angle nonmechanical steering system with fine andcoarse steering modules for azimuthal (AZ) and elevation (EL) directions.

conclude that the SB design will likely produce the highestthroughput large angle steerer.

III. DESIGN PARAMETERS OF 1D/2D STEERING

A conceptual configuration of nonmechanical beam steeringsystem is shown in Fig. 3. This includes a fine steering module[22], [23] to steer an input beam within comparably small an-gles (e.g., ±5◦), and a coarse steering module, which is whatwe focused on in this paper, in order to steer the output beam ofthe fine module to cover larger FOR (e.g., ±45◦ or larger). Bothfine and coarse steering modules may include sub-assembliesfor different steering dimensions (i.e., AZ, EL). The AZ andEL parts in the coarse steerer contain the same elements in thesame configuration, but the grating directions of each part are or-thogonal to each other (e.g., ΨAZ = 0◦, ΨEZ = 90◦). When theangle parameters for both the fine and coarse modules are cho-sen properly, the steering system can maximize the total FOR,and steer into any angle within the FOR within the resolutionof the fine steering module.

A. 1D Steering

First, we consider the simplest case: one dimensional (1D)steering. Fig. 4(a) shows a single steering stage that comprises aswitchable LC WP and a polymer PG resulting in two-way steer-ing. When the input light is circularly polarized, the WP ensuresthat the input to the PG is either of the two orthogonal circularpolarization states (i.e., LCP: Left handed Circular Polariza-tion; RCP: Right handed Circular Polarization). Depending onthe handedness of polarization, the PG diffracts the beam intoone of the two possible orders and flips its handedness. Since thepolymer PG is a passive element, there is ideally no zero-order(0◦ steering angle) present.

To achieve more steering angles, our beam steerer comprisesmultiple stacked stages of this WP/PG assembly. Fig. 4(b) showsa 1D design with three stages (N = 3), where each coarse stagehas a different grating period and can access a different setof angles. Compared to prior multistage diffractive approaches[24], [25], which shave stages with merely one deflecting stateand a non-deflecting state, the PG based steering enables farmore angles to be steered by the same number of stages. In thelatter, the total number of steering angles M is determined by

Fig. 4. Polymer PG based 1D steering: (a) Two-way beam steering in singlesteering stage containing a WP and a polymer PG. (b) 1D steering with a fineangle module and a coarse angle module with three-stage (N = 3).

the number of stages N :

M = 2N . (5)

We show this behavior in Fig. 4(b).The fine angle steering module compliments the coarse angle

module by steering much smaller angles, which enables a highresolution FOR. It is important to note that the final steeringangle is a summation of both the fine and coarse steering an-gles. Therefore, it is important to properly choose the angles ofthe coarse steerer to avoid overlapping steering angles when thecoarse module is combined with the fine module. Here we con-sider the coarse angle separation in direction cosine space, sincethe angles can be described by a simple linear vector represen-tation in the cosine space. The coarse steering angle resolutionr is determined by the number of steering angles M and theFOR:

r =2 sin (FOR/2)

M. (6)

To achieve optimal resolution r in the direction cosine spacefor the coarse steerer, the first stage should have a diffractionangle equal to half the resolution and every subsequent stageshould have double the diffraction angle of the previous stagein the direction cosine space. This means that the angle of eachstage should be as Ω1 = 0.5r; Ω2 = r; Ω3 = 2r, where Ωl isthe diffraction angle of each lth stage in direction cosine space.Therefore, the PG diffraction angles in the coarse module aregiven by

Ωl = 2(l−2)r (7a)

θl = sin−1 (Ωl) , (7b)

where Ωl and θl are the lth stage PG diffraction angles in direc-tion cosine space and real space respectively.


Fig. 5. Steering angle distributions of the three-stage (N = 3) 1D steer-ing in direction cosine space; red and blue dots represent a coarse and final(fine+coarse) steering respectively.

To cover total FOR (i.e., 2 sin(FOR/2) in cosine space),the fine steering module should point the beam into an anglewithin±θ1 (i.e., within r in cosine space). Then, the 1D steeringangles can be spread uniformly as shown in Fig. 5 withoutany unnecessary overlap of the steering angles; the blue dotsrepresent the final 1D steering angles. The final angle Θ1D canbe expressed as

Θ1D = sin−1(

sin θf +N∑

l=1

(−1)Vl sin θl

)

, (8)

where θf is the steering angle of the fine module, and Vl is thestate of the lth WP (0 or 1 when the WP output is LCP or RCP,respectively).

If we assume that the efficiency and loss of each stage is thesame, we can approximate the system transmittance T1D in thefollowing way:

T1D = (η+1)N (1 − D)N (1 − R)2N (1 − A)N Tf , (9)where η+1 is the experimental intrinsic diffraction efficiency[13] of each polymer PG, D is the diffuse scattering of each PG,and R is the Fresnel reflectance of each element (LC waveplate+ polymer PG), A is the absorption losses of each LC element(LC waveplate only), and Tf denotes the throughput of the finesteering module.

B. 2D Steering

2D steering is an extension of 1D steering with cascadedadditional fine and coarse steering modules with orthogonalorientation. When the angle parameters of the two orthogonal 1Dmodules are the same, we can draw the steering map in directioncosine space as shown in Fig. 6(a). This is the 2D version ofthe angle distribution shown in Fig. 5. Here we consider N = 2for the 2D coarse steering module, which can steer a beam to16 coarse angles (red dots). As the coarse steering is combinedwith the fine steering, the beam can be steered into any of thefinal angles (blue dots) within the total FOR. Fig. 6(b) showsthe steering map of the 2D steering in real space. The finalsteering angles of the region (1,1) are shown on those steeringmaps as an example.

Note that the maximum steering angle is in the diagonaldirection. For example, the 2D steerer with a two-stage coarsesteerer (N = 2, θf = 10.2◦, θ1 = 10.2◦, θ2 = 20.7◦) can cover

Fig. 6. Steering angle distributions of the two-stage (N = 2) 2D steering in(a) direction cosine space and (b) real space; red and blue dots represent a coarseand final (fine+coarse) steering respectively. Final steering angles only in theregion (1, 1) are shown.

90◦ FOR in the horizontal and vertical directions (e.g., φ =0◦, 90◦) but it covers 180◦ FOR in the diagonal direction (e.g.,φ = 45◦, 135◦).

While here we assume the same FOR for the two orthogonal1D modules, which leads to a symmetric FOR in the directioncosine and real spaces, the FOR of the 1D modules can bedifferent, which causes an asymmetric final FOR that might beconsidered depending on the application.

For all cases, the final steering angle can be estimated asbelow. The direction cosines of the steered beam are given by

αout = ΩAZfine +N∑

l=1

(−1)V A Zl ΩAZl (10a)

βout = ΩELfine +N∑

l=1

(−1)V E Ll ΩELl , (10b)

where ΩAZ (EL)fine = sin θAZ (EL)fine is the fine steering angle in co-

sine space, ΩAZ (EL)l is the lth single steering stage angle incosine space of the AZ(EL) coarse module, and V AZ (EL)l is thestatus of the lth WP in AZ(EL) coarse module (0 or 1 when theWP output is LCP or RCP, respectively). Then, the final outputazimuthal angle Φ2D and polar angle Θ2D in the real space canbe calculated as

Φ2D = tan−1 (βout/αout) (11a)


Fig. 7. The number of steering angles and calculated transmittance versusnumber of stages of the 2D SB steering design. Three cases of {η+1 , D, R, A}in Eq. (12) are shown, as described in the text.

Θ2D = cos−1(√

1 − α2out − β2out)

. (11b)

Like the 1D steering case, we can approximate the overallsystem transmittance T2D of the 2D steerer in the followingway:

T2D = (η+1)N′(1 − D)N ′(1 − R)2N ′(1 − A)N ′TAZf TELf ,

(12)where N ′ = NAZ + NEL when NAZ and NEL are the stagenumbers of the 1D modules in AZ and EL respectively, andthe TAZf and T

ELf indicate the throughput of the fine steering

modules in AZ and EL.We graph T2D of symmetric FOR 2D steering for three

cases in Fig. 7. Case (i) corresponds to the best-case scenario,where low loss transparent conductors are employed to reachA = 0.2%. Case (ii) corresponds to the case when commer-cially available index-matched ITO is used, to reduce R to0.1%. Case (iii) corresponds to the parameters we were ableto experimentally demonstrate in this work (e.g., η+1 = 99.5%,D = 1%, R = 1%, and A = 2%). In all cases, we observe aroughly linear decrease in T as N increases.

IV. SIMULATION

A. PG Efficiency Estimation by 3D FDTD Analysis

The diffraction efficiency of a PG is nearly ideal when the in-put incidence is normal to the PG’s surface. However, as shownin the illustration of the steerer (see Fig. 4(b)), the incidenceangle will usually be oblique. At these oblique incidence cases,a PG may have increased zero-order leakage, which may con-tribute significantly to sidelobes in the final steering assem-bly. To minimize the sidelobes of the steerer, we need to studythese non-ideal oblique incidence cases in order to optimizethe assembly configuration. Here we utilize the finite differencetime domain (FDTD) method to simulate and characterize PGs.Specifically, we need a FDTD algorithm capable of handling ar-bitrary 2D, periodic, birefringent, dichroic media with obliquelyincidence sources. We use an open-source FDTD code that wehave developed, called Wolfsim [16], that has these capabilities(in addition to being able to simulate 3D structures).

Fig. 8. Simulated diffraction efficiency (η+1 : first order, η0 zero order) ofPGs for the oblique angle incidence: {θin , φin } = {−50◦ − 50◦, 0◦}, whenthe input is circular polarization. Curves: Λ = 5λ (dotted), Λ = 10λ (dashed),and Λ = 20λ (solid). (inset) FDTD simulation showing magnitude changes ofthe in-plane electric field component as a lightwave propagates through a PGcovered by anti-reflection (AR) coating. θm is the first order diffraction angledescribed in Eq. (2).

Fig. 9. The zero order leakage of the PG (Λ = 10λ) for oblique angle inci-dence (e.g., < ±45◦ polar and full azimuthal angle).

The simulated PGs have average index n = 1.5, birefrin-gence Δn = 0.13, thickness d = λ/2Δn, and various periods:(i) Λ = 5λ, (ii) Λ = 10λ, and (iii) Λ = 20λ. The oblique an-gle of the source follows the grating vector of the PGs and thesource was right-hand circular polarized. The simulation gridsize varied slightly for each period, but was about 200 × 250,and obtaining the entire hemisphere plot (with high degree of ac-curacy) took a number of hours. The simulation result in Fig. 8shows that there is decreased first order efficiency (i.e., lead-ing to the mainlobe) and increased zero-order efficiency (i.e.,leading to the sidelobe), with the trend increasing for higherincidence angles. It is noteworthy that the maximum efficiencycase occurs slightly off-axis. However, if the polarization of theinput beam is reversed, this same angle becomes non-ideal (i.e.,Fig. 8 would be mirrored).

For 2D steering with AZ and EL steering modules, wemust consider the impact on efficiency due to arbitrary whole-hemisphere incidence (i.e., Φ ≤ 360◦ and Θ ≤ 90◦). In Fig. 9,we show the simulation results of the zero order leakage re-sponse with angles of incidence θ = 0◦ − 45◦ and φ = 0◦ −360◦. From this plot, it is clear that the diffraction efficiency


is much more effected by in-plane incidence than out-of-planeincidence. This impact was studied by other authors and theysuggested how this can be minimized [26].

Concerning the response characteristics, we note that for φ =90◦ the location of the diffraction maxima and minima shiftonly slightly, while φ = 0◦ shifts them a noticeable amount.With this in mind, we can effectively design a 2D steerer bydesigning two 1D steerers independently and then combiningthem, with minimal loss in efficiency.

B. Beam Steering Efficiency Estimation byRay-Tracing Simulation

We used ray-tracing tool (TracePro, Lambda Research) tosimulate mainlobe and sidelobes efficiency of 2D SB beamsteerer which is based on the optimal design described in SectionIII. A target FOR of the model is 65◦ in 1D with a step of ∼8◦at 1550 nm.

The simulation includes mainly three parts: input source,beam steerer, and detector. First, the input beam in the modelis collimated single wavelength (1550 nm) light with uniformintensity distribution. In the ray-tracing software, 10,000 raysare simulated as the input and they are incident normal to thefront surface of the beam steerer. The beam steerer contains twomodules for different steering directions, azimuth and elevation.Each module includes three steering stages containing switch-able half-waveplates and polymer PGs. Each steering moduledrives eight steps coarse steering in 1D (i.e., Az or El) so thata stack of both modules performs in total 64 steering anglesin 2D. Each PG diffraction angle is selected by the Eq. (7),which achieves equally distributed steering angles in 2D direc-tion cosine space as Fig. 6(a). Other PG properties (e.g., zeroorder leakage on oblique incidence, material absorption, reflec-tion, etc.) for the simulation are determined by the result of theFDTD analysis shown in Section IV-A with our best estimation.A 3D model of the physical arrangement of this model includingthe input and the steerer is shown in Fig. 10(a) and (b).

In the ray-tracing simulation, all of the output rays of the beamsteerer are captured in order to examine steering efficiency ofthe model. We simulated all possible steering angles (M = 64)and the output efficiency (η) of the mainlobe is shown in thepolar plot (see Fig. 10(c)). All of angles showed high steeringefficiency (η ≥ 80%). In Fig. 10(d), moreover, we selectivelydisplayed one of the steering case for the largest steering angle.The mainlobe efficiency of the case (Θ2D = 45◦, Φ2D = 135◦)was∼87%. Any single sidelobe had


TABLE ICHARACTERIZATION DATA OF THE POLYMER PGS USED IN THREE-STAGES

COARSE STEERING WHEN θl AND Λl DENOTE THE DIFFRACTION ANGLE ANDTHE GRATING PERIOD OF lTH PGS.

l θl (◦) Λ l (μm) η+ 1 (%) η0 (%) η−1 (%) Dl (%)

1 3.9 23.1 99.7 0.1 0.1 0.12 7.7 11.5 99.4 0.2 0.2 0.23 15.6 5.8 97.5 1.7 0.4 0.4

Fig. 11. Calculated PG diffraction angles for three-stage (N = 3) 1D coarsesteering. Curves: PG1 (l = 1, solid), PG2 (l = 2, dashed), PG3 (l = 3, dotted).The red line denotes the demonstration for 65◦ FOR.

formed three different PGs with 23.1, 11.5, and 5.8 μm gratingperiods, leading to diffraction angles ±3.9, ±7.7, and ±15.6◦at 1550 nm respectively. The required PG angles for the three-stage, 1D coarse steerer for any FOR are shown in Fig. 11.

Since PGs with larger angles tend to show more leakage atoblique incidence, as we discussed in Section IV, it is oftenpreferred to arrange the largest angle PG can be placed first inthe steering assembly (i.e., closest to the source) to minimizethe sidelobes of the steerer. Doing so makes the incidence angleof the largest angle PG close to ideal (i.e., normal to the PG) allof the time. Likewise, the smallest angle PG can be placed atthe end of the assembly, since it is least impacted by the obliqueincidence.

With the three PGs prepared and three switchable LC WPs[14] optimized for 1550 nm wavelength (fabricated in-house),we assembled the 1D coarse steering module shown as the Fig. 4with the order of PG3 (adjacent to the input), PG2, and PG1consecutively. To minimize reflection loss, all elements werelaminated to each other with optical glue (NOA-63, Norland),and glass with anti-reflection coating (PG&O) was glued to thefront and back faces. The resulting steering module was ∼1 cmthick.

C. Scalable Interferometric Approaches for Creating PGs

A PG can be recorded using the interference of two or-thogonally circular polarized beams [17], [18]. Fig. 12(a)is a schematic illustration of the conventional polarization

Fig. 12. (a) Conventional polarization holography setup. (b) Interferometricholography setup with a non-polarizing beam splitter (NPBS), mirrors (M),and quarter-waveplates (QWP). (c) Schematic illustration of the incoming andoutgoing beams in the NPBS. (d) A picture of the actual optics setup of theinterferometric scheme.

holography setup. The QWPs with orthogonal slow-axes (e.g.,+45◦ and−45◦ w.r.t. input linear polarization) change the polar-ization state of the two recording beams to be orthogonal circular(i.e., left- and right-handed) polarizations. The two beams areoverlapped on the sample area and make an interference patternwhich is then used to create the holographic grating structures.When the beams are projected on the sample with a recording an-gle θR , they generate spatially varying linear polarization fieldswith a periodicity determined by Bragg’s Law: Λ = λ/2 sin θRwhere λ is the recording wavelength. In this configuration, themaximum achievable active area of the recording hologram isequal to the distance D. The recording length L increases as Dincreases and as Λ increases as described below:

L =D

2 tan(asin(λ/2Λ)). (13)

As an example, to fabricate a PG having a 100 μm grating periodand a 100 mm active area with a He-Cd UV (λ = 325 nm) laser,the classic setup requires around 30 m exposing distance, whichis difficult to achieve practically.


Fig. 13. Normalized transmittance spectrum (measured) of the PG2 (l = 2)optimized for 1550 nm wavelength; (inset) measured output wavefront of thefirst order of the PG.

To overcome the above limitations, we propose a new ap-proach that is scalable and can reduce the exposure distancesignificantly by utilizing a Michelson interferometric configu-ration as shown in Fig. 12(b). A linearly polarized input beamfrom a UV laser is converted into RCP after passing through aQWP with +45◦ axis. Then the beam is split by the NPBS wherethe polarization of one of the beams is converted to LCP after itpasses through other QWP twice upon reflection from a mirror.Both beams are recombined by the same NPBS and cause anoverlap at the sample area where a PG pattern is recorded.

This holographic method utilizes a NPBS to control therecording angle θR . This is illustrated in Fig. 12(c) where arotation of the NPBS (θ) causes a change of the recording angleby a factor of 2 (i.e., θR = 2θ). This method allows for recordingvarious grating periods without changing any position and sizeof the optics. Moreover larger active area can be obtained with-out increasing distance between optics. The only requirement isincreasing the beam size and the size of the polarizing optics.Based on this new technique and 100 mm diameter optics, weexperimentally fabricated PGs with various periods (e.g., 5–100μm) within 30 cm2 space. Some of the PG samples were usedfor making a prototype beam steering module shown in SectionVI. Fig. 12(d) shows a picture of the setup with the change ofthe polarization status. The input beam split by the NPBS trav-els different beam paths (i.e., red and blue) and the split beamsmake a PG pattern on the sample area.

VI. EXPERIMENTAL RESULTS

A. Individual PG Characterization

Fig. 13 shows the first- and zero-order spectrum of the 11.5μm PG, which is comparable to Eq. (1). In order to measure theoutput wavefront of the first-order diffracted wave, we used aShack–Hartmann wavefront sensor (Thorlabs) with He-Ne laser(633 nm). The inset of Fig. 13 shows the output wavefront for4 mm2 region of the PG. The average output wavefront qualityover nine different regions of the sample was fairly uniform(e.g., P-V λ/10, RMS λ/39, STD 0.023) compared to the output

Fig. 14. Experimental results of the three-stage coarse steerer optimized for1550 nm: (a) A picture of the coarse steerer assembly; (inset, left) a pictureof ceiling light; (inset, right) diffraction of the ceiling light through the steererassembly. (b) A composite image of photographs of the 8 steered beams on anIR-viewing card. (c) Steering efficiency and transmittance of the mainlobe atall output angles; the sidelobes are shown only for the case where the mainlobehas the largest steering angle.

wavefront of the bare substrate (P-V λ/20, RMS λ/68, STD0.011).

Table I shows measured diffraction efficiencies of the threefabricated PGs with an infrared laser (1550 nm, 40 mW). Theinput is circularly polarized and incident normal to the surface.In order to obtain an experimental quantity η, we define theabsolute diffraction efficiency of order m as ηm = Pm /Ptotwhere Pm is the measured power of the mth diffraction order andPtot is the measured total output power of the sample, measuredwith an integrating sphere (Newport). We define the scatteringloss D as the fraction of transmitted light that does not appearwithin one of the three diffraction orders (+1, 0,−1). ThesePGs exhibit nearly ideal diffraction properties;≥ 97.5% of inputlight is steered into the intended direction without observablehigher orders (η0 ≤ 1.7%, η−1 ≤ 0.4%).

B. Steering Module Performance

We assembled a prototype polymer PG-based 1D beam steer-ing module with three steering stages, which covers 65◦ FORwith ∼8◦ resolution at 1550 nm wavelength. Fig. 14(a) shows


Fig. 15. Measured dynamic response of SLCVR

a picture of the assembly (25 × 25 × 10 mm). The inset showsceiling light images without and with the assembly set 45◦ fromthe horizontal. Since the assembly was optimized for the IR(1550 nm), the ceiling light (VIS) was diffracted into multipleimages. Fig. 14(b) shows the images of the steered beams fromthe coarse module, which are captured by an IR-viewing sensorcard. We fixed the position of the camera and took each steeredbeam projected on the card that was 5 cm away from the assem-bly. The beam was selectively steered as applying the voltageon the WPs as described in Section III, and a steering time ofthe prototype was less than 10 ms as reported [27].

The measured transmittance and diffraction efficiency of themainlobe are shown in Fig. 14(c). The measured transmittance,comparable to Eq. (9), is calculated as T = Pmain/Pin , wherePmain is the mainlobe power and Pin is the input power. The effi-ciency, a normalization that removes the effect of the substratesto reveal the aggregate effect of the diffractive PGs, is definedas η = Pmain/Ptot . For all steering angles, strong transmittance(84–87%) was observed, along with high diffraction efficiency(93–96%). This confirms that losses in this demonstration arepredominantly related to the substrate absorption and reflection,and that the PGs are fairly efficient at redirecting light as ex-pected even when the incidence angle is far from the normaldirection. Reflectance and absorption is primarily due to thetransparent-conducting-electrode material and interfaces withineach WP and PG; the LC itself has comparatively very low ab-sorption. We also show the relative transmitted power across theobserved output angle range ±40◦ for the largest steering angle(the worst case). As shown in Fig. 14(c), all sidelobes were lessthan 1.5% and in the worst case totaled 4.4%. These sidelobesrelate to the oblique incidence on the PGs, and likely can bereduced by employing specialized wide-angle PGs [26], higherbirefringence materials, and/or compensation films.

C. Steering With a Swift LC Variable Retarder

The switchable element of the SB steerer is the half-waveretarder, which is used in each steering stage. Therefore, theswitching speed only depends on the switching speed of thisretarder. Here we demonstrate fast beam steering of our sin-gle steering stage with a swift LC variable retarder (SLCVR,

Meadowlark Optics Inc). We arranged the SLCVR in front ofa polymer PG, as illustrated in Fig. 4(a), and measured the dy-namic response of the first order diffraction efficiency from thePG. While this is a switching time measurement of a singlestage, the result is characteristic of any number of stages, sincethey would be switched in parallel. The response time (10–90%)is less than 2 ms (


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[27] J. Buck, S. Serati, L. Hosting, R. Serati, H. Masterson, M. J. Escuti, J. Kim,and M. N. Miskiewicz, “Polarization gratings for non-mechanical beamsteering applications,” Proc. SPIE, vol. 8395, pp. 83950F-1–83950F-6,Jun. 2012.

Jihwan Kim (M’09) received the M.S. and Ph.D. degrees in electrical engineer-ing from North Carolina State University (NCSU), Raleigh, NC, USA, in 2011.He is currently a Postdoctoral Research Scholar of electrical and computer engi-neering at NCSU. His research and professional interests include optics and pho-tonics, especially on using liquid crystal and functional polymers to investigateand develop transformational diffractive optics and polarization-independentdevices and systems, including high-efficiency/portable liquid crystal displays,ultraefficient energy directing/beam steering for high energy applications andlaser communications, and VIS/IR hyperspectral imaging polarimetry. He haspublished more than 19 refereed journal/conference publications and two issuedand three pending US patents.

Dr. Kim received the SPIE (International Society for Optics and Photonics)Scholarship in Optical Science and Engineering in 2010 and served as a Presi-dent for the NCSU chapter of SPIE in 2011.

Matthew N. Miskiewicz (M’13) received the Ph.D. degree in electrical engi-neering from North Carolina State University, Raleigh, NC, USA, in 2014. Hisresearch interests include FDTD methods, polarization holography, computer-generated holograms, beam-combining, beam-shaping, beam-steering, noveldirect-write systems, and liquid crystal physics. His professional experience in-cludes three years at Progress Energy (now Duke Energy) where he worked onprojects related to fire protection, probability risk analysis, electrical metering,and data management systems. For a short time, he was a subcontractor doingsoftware development.

Dr. Miskiewicz is a Member of the SPIE, Tau Beta Pi, and Eta Kappa Nu.He served as an Officer for the NCSU chapter of Eta Kappa Nu for three yearsand was an active member of the electrical engineering student body.

Steve Serati received the B.S. and M.S. degrees in electrical engineering fromthe Montana State University, Bozeman, MT, USA, in 1983. He is a Founder andPresident of Boulder Nonlinear Systems Inc. (BNS) at Boulder, Lafayette, CO,USA. Before starting BNS in 1988, he spent five years with Honeywell, Inc.,Avionics Division, three years with OPHIR Corporation, and two years withTycho Technology, Inc. During his tenure at Honeywell, he worked on radaraltimeters and target-tracking coherent Doppler radar systems. At OPHIR, hedeveloped the digital and analog electronics for a variety of meteorologicalsensors including humidity sensors, icing detectors, ladar, and LDV systemsand managed some of the sensor development programs. While at Tycho, heperformed the dual function of program management and system engineeringfor the development, manufacturing, and testing of large (500-kilowatt) UHFand VHF Doppler radar systems that profile atmospheric conditions (clear-airwinds and turbulence). In his current position as BNS President, he is also thePrincipal Investigator for developing nonmechanical beam steering techniquesfor active and passive systems and is responsible for improving spatial lightmodulator technologies that are being used for holographic optical trapping, 3-D photostimulation and laser marking, superresolution imaging, pulse shaping,and wavefront correction. He is the author on more than 50 technical papers,one book chapter, and four patents.

Michael J. Escuti (M’02) received the Ph.D. degree in electrical engineer-ing from Brown University, Providence, RI, USA, in 2002. He is currently anAssociate Professor of electrical and computer engineering at North CarolinaState University (NCSU), Raleigh, NC, USA, where he pursues interdisciplinaryresearch topics in photonics, optoelectronics, flat-panel displays, diffractive op-tics, remote sensing, and beyond. He is a named Inventor on 11 issued and19 pending US patents. He has published more than 103 refereed journal andconference publications, has presented 29 invited research talks, and has coau-thored one book chapter. He has been recognized by the 2010 Presidential EarlyCareer Award for Scientists and Engineers, National Science Foundation CA-REER Award, the Alcoa Foundation Engineering Research Achievement Award(2011) for his work at NCSU, and both the Glenn H. Brown Award (2004) fromthe International Liquid Crystal Society and the OSA/New Focus Student Award(2002) from the Optical Society of America at the CLEO/QELS Conference forhis Ph.D. research.

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